Shocks and induced discontinuities in materials with internal state variables - Applications to finite linear viscoelasticity
In this paper, we derive the coupled governing differential equations of shock amplitudes and induced discontinuities in materials with internal state variables. For the special case of finite linear viscoelasticity and weak shocks and under physically reasonable conditions, two examples of the solutions of the coupled equations are given. In the first example, the solutions of the shock and the induced discontinuity approach finite non-zero values in an oscillatory manner, very much akin to the forced vibrations of spring-mass-damper systems. In the second example, both solutions decay monotonically to zero.
necessary condition for existence of steady shock
coupled governing differential equations
scientific article; zbMATH DE number 3940838